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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.01976 |
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| _version_ | 1866909060872273920 |
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| author | Beachy, John A |
| author_facet | Beachy, John A |
| contents | For an associative ring we investigate a construction of Cohn's universal ring of fractions defined relative to a multiplicative set of matrices. The construction avoids the Ore condition, which is necessary to construct a ring of fractions relative to a multiplicative set of elements. But a similar condition, which we call the ``pseudo-Ore'' condition, plays an important role in the construction of Cohn's localization. We show that this condition in fact determines the equivalence relation used in the construction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01976 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the construction of Cohn's universal localization Beachy, John A Rings and Algebras 16S10 For an associative ring we investigate a construction of Cohn's universal ring of fractions defined relative to a multiplicative set of matrices. The construction avoids the Ore condition, which is necessary to construct a ring of fractions relative to a multiplicative set of elements. But a similar condition, which we call the ``pseudo-Ore'' condition, plays an important role in the construction of Cohn's localization. We show that this condition in fact determines the equivalence relation used in the construction. |
| title | On the construction of Cohn's universal localization |
| topic | Rings and Algebras 16S10 |
| url | https://arxiv.org/abs/2401.01976 |